A photolithographic exposure apparatus for manufacturing a semiconductor element such as an LSI, a liquid crystal display element, a thin film magnetic head or the like is configured to perform exposure by irradiating light from a light source onto a pattern on a projection original plate such as a mask or a reticle through an illumination optical system, and by projecting the pattern onto a photosensitive substrate such as a wafer or a glass plate coated with a photoresist in advance through a projection optical system. The types of the projection optical system include a dioptric projection optical system including lenses for transmitting and refracting light having an exposure wavelength, a catoptic projection optical system including a mirror for reflecting the light having the exposure wavelength, and a catadioptric projection optical system combining the lenses and the mirror.
In recent years, the integration degree of semiconductor elements and the like is increasing and patterns to be transferred onto substrates are continuously getting smaller. Accordingly, a photolithographic exposure apparatus has been changing its light source from the i-line (365 nm), the KrF excimer laser (248 nm), the ArF excimer laser (193 nm), and further to the F2 laser (157 nm) to progress the shortening of wavelengths. In this concern, there is a growing demand for the photolithographic exposure apparatus in the optical system to achieve a higher optical performance. In particular, there is a demand for the projection optical system, which is configured to transfer a fine mask pattern onto a photosensitive surface of a wafer, to achieve extremely high optical performance at high resolution and with very little aberration. To meet this demand, there is a growing demand for an extremely high level of refractive index homogeneity in optical members including lenses, prisms, mirrors, photomasks, and the like (hereinafter, optical members for photolithography) used as an optical system of a photolithographic exposure apparatus.
Conventionally, evaluation of refractive index homogeneity of an optical material for photolithography has been conducted by measuring a wavefront aberration generated when light passes through the optical material and defining a difference between a maximum value and a minimum value of the wavefront aberration (hereinafter referred to as a PV value) or a root mean square value (hereinafter referred to as an RMS value) as an evaluation index. To be more precise, it has been considered that a more excellent optical material had a smaller PV value or RMS value. That is, an optical material to be categorized in high quality has been manufactured by way of reducing these values.
For example, Japanese Unexamined Patent Application Publication No. Hei 8-5505 (JP 8-5505 A) discloses the following evaluation method of the refractive index homogeneity. Concrete procedures of this method are described below.
(Procedure 1) An optical material for photolithography polished into a column or a prism shape is set on an interferometer, and a reference wavefront is emitted perpendicularly to a polished surface to measure the wavefront aberration. Information attributable to refractive index distribution of the optical material appears on the measured wavefront aberration. Of the measured wavefront aberration, an error aberration attributable to a curvature component is called either as a power component or a focus component, while an error aberration attributable to a gradient component is called as a tilt component.(Procedure 2) The power component and the tilt component are removed from the measured wavefront aberration.(Procedure 3) Moreover, a wavefront aberration attributable to an astigmatism component is removed.(Procedure 4) The remaining wavefront aberration is split into a rotationally symmetric component and a non-rotationally symmetric component (a random component).(Procedure 5) The PV value and the RMS value of the non-rotationally symmetric component (the random component) are obtained, and evaluation is carried out based on these values.(Procedure 6) The rotationally symmetric component is fitted to an aspheric formula with the least square method to remove quadratic and biquadratic components. The PV values and the RMS values for remaining sextic and higher even-ordered wavefront aberration components (hereinafter referred to as a quadratic-biquadratic residual error) are found. Then, evaluation is carried out based on these values.
As it is apparent from the above-described procedures, an optical material having the small non-rotationally symmetric component (the random component) and the small quadratic-biquadratic residual error, has been deemed as an excellent optical material in the refractive index homogeneity, and efforts have been made to manufacture such an optical material.
Upon construction of an optical system, multiple pieces of optical members manufactured by use of the optical materials evaluated as described above are combined together. Concerning evaluation of an imaging performance of the optical system thus constructed, Japanese Unexamined Patent Application Publication No. 2000-121491 proposes a fitting method applying a Zernike's cylinder function system. In this method, evaluation is carried out by measuring the wavefront aberration while allowing the light to pass through the optical system, fitting (expanding) those data to the Zernike's cylinder function system, and classifying them into respective components of a rotationally symmetric component, an odd-number rotational component, and an even-number rotational component. The respective components of the rotationally symmetric component, the odd-number rotational component, and the even-number rotational component have strong correlations with a spherical aberration, a coma aberration, and astigmatism, respectively. Accordingly, it is possible to carry out the evaluation of the optical system directly in association with the imaging performance.
Meanwhile, International Publication No. 03/004987 (WO 2003-004987 A) discloses a method of evaluating inhomogeneity of refractive indices of individual optical members constituting an optical system by utilizing Zernike expansion of wavefront aberrations.